BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES  

作　　者：林路 张润楚 

机构地区：[1]School of Mathematics and system Scences, shandong University,Jinan 250100, China School of Mathematical Sciences, Nankai University, Tianjin 300071. China [2]School of Mathematics and System Science, Shandong University, Jinan 250100, China

出　　处：《Acta Mathematica Scientia》2004年第1期61-70,共10页数学物理学报（B辑英文版）

基　　金：This paper is supported by NNSF project(10371059);China and Youth Teacher Foundation of Nankai University

摘　　要：This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.

关 键 词：Nonparametric regression weakly dependent process BOOTSTRAP WAVELET 

分 类 号：O241[理学—计算数学]